Weak type inequalities for moduli of smoothness: The case of limit value parameters

DOI10.1007/s00041-009-9101-1zbMath1217.41015OpenAlexW2066528891MaRDI QIDQ992027

Sergey Yu. Tikhonov

Publication date: 8 September 2010

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-009-9101-1

zbMATH Keywords

K-functionalsembeddings of Lipschitz-type spacesmoduli of smoothness of fractional orderUl'yanov-type inequalities

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (14)

Refinement of the relations between mixed smoothness moduli in \(L_1\) and \(L_q\) metrics ⋮ Interrelations between partial moduli of smoothness in various mixed metrics ⋮ Continuous and Compact Embeddings of Bessel-Potential-Type Spaces ⋮ Refinement of relations between mixed moduli of smoothness in the metrics of \(L_p\) and \(L_\infty \) ⋮ Some recent developments in the theory of function spaces involving differences ⋮ Improvement of relations between moduli of smoothness ⋮ Ulyanov-type inequalities between Lorentz-Zygmund spaces ⋮ Connection between moduli of smoothness in the metrics of \(L_p\) and \(C\) ⋮ Sharp Ul'yanov inequalities for generalized Liouville-Weyl derivatives ⋮ Some Problems in Fourier Analysis and Approximation Theory ⋮ Analogues of Ulyanov Inequalities for Mixed Moduli of Smoothness ⋮ Embeddings of function spaces: a criterion in terms of differences ⋮ Properties of moduli of smoothness in \(L_p (\mathbb{R}^d)\) ⋮ Jacobi weights, fractional integration, and sharp Ulyanov inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Best approximation and moduli of smoothness: Computation and equivalence theorems
• Nikol'skii inequalities for Lorentz spaces
• Weak interpolation in Banach spaces
• Ul'yanov and Nikol'skii-type inequalities
• Moduli of smoothness and \(K\)-functionals in \(L_ p\), \(0<p<1\)
• Convergence of trigonometric series with general monotone coefficients
• An Approach to Fractional Powers of Operators via Fractional Differences
• Best Trigonometric Approximation, Fractional Order Derivatives and Lipschitz Classes
• On riesz-type inequalities and k-functionals related to riesz potentials in
• On Inequalities of Periodic Functions and Their Derivatives
• Embeddings of fractional Sobolev spaces and estimates of Fourier transforms
• On multipliers preserving convergence of trigonometric series almost everywhere

This page was built for publication: Weak type inequalities for moduli of smoothness: The case of limit value parameters